Integral p-adic Hodge Theory of Perfectoid Shimura Varieties in the Symplectic Quantization of Superluminal Alcubierre-White Warp Drive Spacetimes
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| Language: | English |
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2025
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| author | MFC, 10 Revista, Zen |
| author_facet | MFC, 10 Revista, Zen |
| contents | <p>Mathematical Applications of Science Fiction</p> <p>We present a rigorous derivation of the stability conditions for superluminal Alcubierre-<br>White warp drive spacetimes by mapping the Lorentzian manifold singularities to the non-<br>Archimedean geometry of Perfectoid Shimura Varieties. While classical General Relativity<br>predicts the violation of the Null Energy Condition (NEC) requiring exotic matter with<br>negative energy density, we propose that at the sub-Planckian scale (L < Lp), the spacetime<br>metric undergoes a topological phase transition from a smooth Riemannian manifold MR to<br>a Perfectoid space Xperf over Qp. By employing the Scholze-Andrade tilting correspondence,<br>we construct a canonical isomorphism between the symplectic phase space of the warp bubble<br>and the cohomology of a specific class of Shimura varieties of infinite level.<br>We introduce the concept of "Arithmetic Warp Quantization," where the Casimir energy<br>density required to sustain the warp bubble is regularized via the p-adic L-functions associated<br>with the automorphic representations of the group GSp2g. We prove that the divergence of<br>the stress-energy tensor Tμν is merely an artifact of Archimedean valuation and vanishes<br>in the crystalline cohomology of the associated Fargues-Fontaine curve. Furthermore, we<br>utilize Integral p-adic Hodge Theory to define a "Period Ring of Causality," Bcaus, showing<br>that closed timelike curves (CTCs) are eliminated by the monodromy action on the étale<br>cohomology groups Hi<br>´et(X, Zp).<br>This manuscript establishes three fundamental theorems: (1) The Perfectoid Stability<br>Criterion, which links the warp bubble’s horizon stability to the Galois representations of the<br>absolute Galois group GQp; (2) The Symplectic Quantization Theorem, deriving the discrete<br>spectrum of warp velocities allowed by the arithmetic of the Shimura variety; and (3) The<br>Causal Protection Theorem, demonstrating that superluminal travel is topologically protected<br>against paradoxes via the vanishing of the first cohomology group of the causal structure sheaf.<br>This work provides the necessary mathematical foundation for the engineering of metric<br>propulsion systems in the post-2050 era, bridging the Langlands Program with Quantum<br>Gravity.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18089145 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Integral p-adic Hodge Theory of Perfectoid Shimura Varieties in the Symplectic Quantization of Superluminal Alcubierre-White Warp Drive Spacetimes MFC, 10 Revista, Zen <p>Mathematical Applications of Science Fiction</p> <p>We present a rigorous derivation of the stability conditions for superluminal Alcubierre-<br>White warp drive spacetimes by mapping the Lorentzian manifold singularities to the non-<br>Archimedean geometry of Perfectoid Shimura Varieties. While classical General Relativity<br>predicts the violation of the Null Energy Condition (NEC) requiring exotic matter with<br>negative energy density, we propose that at the sub-Planckian scale (L < Lp), the spacetime<br>metric undergoes a topological phase transition from a smooth Riemannian manifold MR to<br>a Perfectoid space Xperf over Qp. By employing the Scholze-Andrade tilting correspondence,<br>we construct a canonical isomorphism between the symplectic phase space of the warp bubble<br>and the cohomology of a specific class of Shimura varieties of infinite level.<br>We introduce the concept of "Arithmetic Warp Quantization," where the Casimir energy<br>density required to sustain the warp bubble is regularized via the p-adic L-functions associated<br>with the automorphic representations of the group GSp2g. We prove that the divergence of<br>the stress-energy tensor Tμν is merely an artifact of Archimedean valuation and vanishes<br>in the crystalline cohomology of the associated Fargues-Fontaine curve. Furthermore, we<br>utilize Integral p-adic Hodge Theory to define a "Period Ring of Causality," Bcaus, showing<br>that closed timelike curves (CTCs) are eliminated by the monodromy action on the étale<br>cohomology groups Hi<br>´et(X, Zp).<br>This manuscript establishes three fundamental theorems: (1) The Perfectoid Stability<br>Criterion, which links the warp bubble’s horizon stability to the Galois representations of the<br>absolute Galois group GQp; (2) The Symplectic Quantization Theorem, deriving the discrete<br>spectrum of warp velocities allowed by the arithmetic of the Shimura variety; and (3) The<br>Causal Protection Theorem, demonstrating that superluminal travel is topologically protected<br>against paradoxes via the vanishing of the first cohomology group of the causal structure sheaf.<br>This work provides the necessary mathematical foundation for the engineering of metric<br>propulsion systems in the post-2050 era, bridging the Langlands Program with Quantum<br>Gravity.</p> |
| title | Integral p-adic Hodge Theory of Perfectoid Shimura Varieties in the Symplectic Quantization of Superluminal Alcubierre-White Warp Drive Spacetimes |
| url | https://doi.org/10.5281/zenodo.18089145 |